Abstract
We introduce an arithmetic Walsh transform. It is a with-carry analog, based on modular arithmetic, of the usual Walsh transform of Boolean functions. This is part of our continuing effort to define and investigate with-carry analogs of discrete algebraic structures used in various aspects of communications. We develop tools for analyzing arithmetic Walsh transforms. We prove that the mapping from a Boolean function to its arithmetic Walsh transform is injective. We compute the average arithmetic Walsh transforms and the arithmetic Walsh transforms of affine functions.
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Klapper, A., Goresky, M. (2010). A With-Carry Walsh Transform. In: Carlet, C., Pott, A. (eds) Sequences and Their Applications – SETA 2010. SETA 2010. Lecture Notes in Computer Science, vol 6338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15874-2_18
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DOI: https://doi.org/10.1007/978-3-642-15874-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15873-5
Online ISBN: 978-3-642-15874-2
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